The volatility is one of the essential characteristics of financial time series, which is vital for the knowledge acquisition from financial data. However, since the high noise and nonsteady features, the volatility identification of financial time series is still a challenging problem. In this paper, from a perspective of granule complex network, a novel approach is proposed to study this problem. First, numeric time series is structured into fuzzy information granules (FIGs), where the segments of time series in each granule would own similar volatility features. Second, by using the transfer relations among granules, granule complex network is to be constructed, which intuitively describes the transfer processes among the different volatility patterns. Third, a novel community detection algorithm is applied to divide the granule complex networks, where granules with frequent mutual transfers would belong to the same granule community. Finally, Markov chain model is carried out to analyze the higher level of transfer processes among different granule communities, which would further describe the larger-scale transitions of volatility in overall financial time series. An empirical study of the proposed system is applied in the Shanghai stock index market, where volatility patterns of financial data can be effectively acquired and the corresponding transfer processes can be analyzed by means of the granule communities.

中文翻译：

---

基于颗粒复杂网络的金融时间序列波动性

波动性是金融时间序列的基本特征之一，对于从金融数据中获取知识至关重要。然而，由于具有高噪声和非稳态特征，金融时间序列的波动率识别仍然是一个具有挑战性的问题。本文从颗粒复杂网络的角度，提出了一种新的方法来研究这个问题。首先，数字时间序列被构造成模糊信息颗粒（FIG），其中每个颗粒中的时间序列片段将具有相似的波动性特征。其次，利用颗粒之间的传递关系，构建颗粒复杂网络，直观地描述不同波动模式之间的传递过程。第三，采用一种新颖的社区检测算法来划分粒状复杂网络，其中频繁相互转移的粒状将属于同一个粒状社区。最后，通过马尔可夫链模型分析不同颗粒群落之间更高层次的转移过程，这将进一步描述整个金融时间序列中波动性的更大规模转变。对该系统的实证研究应用于上海股票指数市场，可以有效地获取金融数据的波动模式，并可以通过粒子群落分析相应的传递过程。通过马尔可夫链模型分析不同颗粒群落之间更高层次的转移过程，这将进一步描述整个金融时间序列中波动性的更大规模转变。对该系统的实证研究应用于上海股票指数市场，可以有效地获取金融数据的波动模式，并可以通过粒子群落分析相应的传递过程。通过马尔可夫链模型分析不同颗粒群落之间更高层次的转移过程，这将进一步描述整个金融时间序列中波动性的更大规模转变。对该系统的实证研究应用于上海股票指数市场，可以有效地获取金融数据的波动模式，并可以通过粒子群落分析相应的传递过程。